A rectangular container, whose base is a square of side $5\ cm$, stands on a horizontal table, and holds water upto $1\ cm$ from the top. When a cube is placed in the water it is completely submerged, the water rises to the top and $2$ cubic cm of water overflows. Calculate the volume of the cube and also the length of its edge.

 Given:

A rectangular container, whose base is a square of side $5\ cm$, stands on a horizontal table, and holds water upto $1\ cm$ from the top.

When a cube is placed in the water it is completely submerged, the water rises to the top and $2$ cubic cm of water overflows.

To do:

We have to find the volume of the cube and also the length of its edge.

Solution:

Base of the container $= 5\ cm \times 5\ cm$

Volume of the water raised and overflowed $= 5 \times 5 \times 1 + 2$

$= 25 + 2$

$= 27\ cm^3$

This implies,

Volume of the cube $= 27\ cm^3$

Therefore,

The edge of the cube $=\sqrt[3]{27}$

$=\sqrt[3]{3^{3}}$

$=3 \mathrm{~cm}$

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Updated on: 10-Oct-2022

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